Double-diffusive Magnetic Layering

2021 ◽  
Vol 922 (2) ◽  
pp. 195
Author(s):  
D. W. Hughes ◽  
N. H. Brummell
Keyword(s):  
Magnetic Field ◽  
Chemical Elements ◽  
Turbulent Transport ◽  
Linear Instability ◽  
Thermosolutal Convection ◽  
Horizontal Magnetic Field ◽  
Diffusive Regime ◽  
Magnetic Buoyancy ◽  
Double Diffusive

Abstract Double-diffusive systems, such as thermosolutal convection, in which the density depends on two components that diffuse at different rates, are prone to both steady and oscillatory instabilities. Such systems can evolve into layered states, in which both components, and also the density, adopt a “staircase” profile. Turbulent transport is enhanced significantly in the layered state. Here we exploit an analogy between magnetic buoyancy and thermosolutal convection in order to demonstrate the phenomenon of magnetic layering. We examine the long-term nonlinear evolution of a vertically stratified horizontal magnetic field in the so-called “diffusive regime,” where an oscillatory linear instability operates. Motivated astrophysically, we consider the case where the viscous and magnetic diffusivities are much smaller than the thermal diffusivity. We demonstrate that diffusive layering can occur even for subadiabatic temperature gradients. Magnetic layering may be relevant for stellar radiative zones, with implications for the turbulent transport of heat, magnetic field, and chemical elements.

Double-diffusive convection with two stabilizing gradients: strange consequences of magnetic buoyancy

1995 ◽  
Vol 301 ◽  
pp. 383-406 ◽  
Author(s):  
D. W. Hughes ◽  
N. O. Weiss
Keyword(s):  
Magnetic Field ◽  
Active Regions ◽  
Finite Amplitude ◽  
Thermosolutal Convection ◽  
Horizontal Magnetic Field ◽  
Magnetic Diffusivity ◽  
Diffusive Convection ◽  
Mean Pressure ◽  
Magnetic Buoyancy ◽  
Double Diffusive

Instabilities due to a vertically stratified horizontal magnetic field (magnetic buoyancy instabilities) are believed to play a key role in the escape of the Sun's internal magnetic field and the formation of active regions and sunspots. In a star the magnetic diffusivity is much smaller than the thermal diffusivity and magnetic buoyancy instabilities are double-diffusive in character. We have studied the nonlinear development of these instabilities, in an idealized two-dimensional model, by exploiting a non-trivial transformation between the governing equations of magnetic buoyancy and those of classical thermosolutal convection. Our main result is extremely surprising. We have demonstrated the existence of finite-amplitude steady convection when both the influential gradients (magnetic and convective) are stabilizing. This strange behaviour is caused by the appearance of narrow magnetic boundary layers, which distort the mean pressure gradient so as to produce a convectively unstable stratification.

scholarly journals Chaos in models of double convection

1992 ◽  
Vol 237 ◽  
pp. 209-229 ◽  
Author(s):  
A. M. Rucklidge
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Fluid Layer ◽  
Period Doubling ◽  
Thermosolutal Convection ◽  
Two Dimensional ◽  
Lorenz Equations ◽  
Third Order ◽  
Horizontal Magnetic Field

In certain parameter regimes, it is possible to derive third-order sets of ordinary differential equations that are asymptotically exact descriptions of weakly nonlinear double convection and that exhibit chaotic behaviour. This paper presents a unified approach to deriving such models for two-dimensional convection in a horizontal layer of Boussinesq fluid with lateral constraints. Four situations are considered: thermosolutal convection, convection in an imposed vertical or horizontal magnetic field, and convection in a fluid layer rotating uniformly about a vertical axis. Thermosolutal convection and convection in an imposed horizontal magnetic field are shown here to be governed by the same sets of model equations, which exhibit the period-doubling cascades and chaotic solutions that are associated with the Shil'nikov bifurcation (Proctor & Weiss 1990). This establishes, for the first time, the existence of chaotic solutions of the equations governing two-dimensional magneto-convection. Moreover, in the limit of tall thin rolls, convection in an imposed vertical magnetic field and convection in a rotating fluid layer are both modelled by a new third-order set of ordinary differential equations, which is shown here to have chaotic solutions that are created in a homoclinic explosion, in the same manner as the chaotic solutions of the Lorenz equations. Unlike the Lorenz equations, however, this model provides an accurate description of convection in the parameter regime where the chaotic solutions appear.

scholarly journals The Evolution of a Double Diffusive Magnetic Buoyancy Instability

2010 ◽  
Vol 6 (S271) ◽  
pp. 218-226
Author(s):  
Lara J. Silvers ◽  
Geoffrey M. Vasil ◽  
Nicholas H. Brummell ◽  
Michael R. E. Proctor
Keyword(s):  
Three Dimensional ◽  
Shear Velocity ◽  
Horizontal Magnetic Field ◽  
Field Gradients ◽  
Vertical Field ◽  
Magnetic Buoyancy ◽  
Interchange Instability ◽  
Upward Moving ◽  
Buoyancy Instability ◽  
Double Diffusive

AbstractRecently, Silvers et al. (2009b), using numerical simulations, confirmed the existence of a double diffusive magnetic buoyancy instability of a layer of horizontal magnetic field produced by the interaction of a shear velocity field with a weak vertical field. Here, we demonstrate the longer term nonlinear evolution of such an instability in the simulations. We find that a quasi two-dimensional interchange instability rides (or “surfs”) on the growing shear-induced background downstream field gradients. The region of activity expands since three-dimensional perturbations remain unstable in the wake of this upward-moving activity front, and so the three-dimensional nature becomes more noticeable with time.

scholarly journals Cosmic Rays and the Parker Instability

1985 ◽  
Vol 107 ◽  
pp. 361-363
Author(s):  
A.H. Nelson
Keyword(s):  
Magnetic Field ◽  
Cosmic Rays ◽  
Interstellar Medium ◽  
Galactic Halo ◽  
Cosmic Ray ◽  
Interstellar Gas ◽  
Horizontal Magnetic Field ◽  
Magnetic Buoyancy ◽  
Field Lines ◽  
Gas Layer

Parker (1966, 1969, 1979) has shown that the magnetic buoyancy of a uniform horizontal magnetic field will destabilize the Galactic gas layer. Perturbations of the form shown in Fig. 1 will grow in time with the magnetic loops ballooning up into the Galactic halo, and the interstellar gas draining down the field lines to collect in the mid-plane. Parker also showed that if the dynamical effect of the cosmic ray component of the interstellar medium is included, using an isotropic cosmic ray pressure, then the instability is enhanced.

Evolution of Large-Scale Coronal Structures

1994 ◽  
Vol 144 ◽  
pp. 29-33
Author(s):  
P. Ambrož
Keyword(s):  
Magnetic Field ◽  
Field Line ◽  
Large Scale ◽  
Coronal Magnetic Field ◽  
Source Surface ◽  
Solar Cycles ◽  
Characteristic Relationship ◽  
The Magnetic Field ◽  
Coronal Structures

AbstractThe large-scale coronal structures observed during the sporadically visible solar eclipses were compared with the numerically extrapolated field-line structures of coronal magnetic field. A characteristic relationship between the observed structures of coronal plasma and the magnetic field line configurations was determined. The long-term evolution of large scale coronal structures inferred from photospheric magnetic observations in the course of 11- and 22-year solar cycles is described.Some known parameters, such as the source surface radius, or coronal rotation rate are discussed and actually interpreted. A relation between the large-scale photospheric magnetic field evolution and the coronal structure rearrangement is demonstrated.

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